"Simply being a guest on David Letterman's show has been a highlight of my career. I never dreamed that I would follow in his footsteps, though everyone in late night follows Dave's lead. ... I'm thrilled and grateful that CBS chose me. Now, if you'll excuse me, I have to go grind a gap in my front teeth."

The network adds that "Colbert's premiere date as host of The Late Show will be announced after Mr. Letterman determines a timetable for his final broadcasts in 2015."